The shell model Monte Carlo (SMMC) approach enables the microscopic calculation of nuclear state densities in model spaces that are many orders of magnitude larger than those that can be treated by conventional diagonalization techniques. However, it has been difficult to calculate accurate state densities of odd-mass heavy nuclei as a function of excitation energy. This is because of a sign problem that arises from the projection on an odd number of particles at low temperatures, making it difficult to calculate accurate ground-state energies of odd-mass nuclei in direct Monte Carlo calculations. Here we extract the ground-state energy from a one-parameter fit of the SMMC thermal energy to the thermal energy that is determined from experimental data. This enables us to calculate the state densities of the odd-even isotopes ${}^{149–155}\mathrm{Sm}$ and ${}^{143–149}\mathrm{Nd}$ as a function of excitation energy. We find close agreement with state densities extracted from experimental data. Our results demonstrate that the state densities of the odd-mass samarium and neodymium isotopes can be consistently reproduced using the same family of Hamiltonians that describe the neighboring even-mass isotopes within the configuration-interaction shell model approach.

The exact nature of the lowest $K^{\pi }=2^{+}$ rotational bands in all deformed nuclei remains obscure. Traditionally they are assumed to be collective vibrations of the nuclear shape in the γ degree of freedom perpendicular to the nuclear symmetry axis. Very few such γ bands have been traced past the usual backbending rotational alignments of high-$j$ nucleons. We have investigated the structure of positive-parity bands in the $N=90$ nucleus ${}^{156}\mathrm{Dy}$, using the ${}^{148}\mathrm{Nd}\left({}^{12}\mathrm{C},4n\right){}^{156}\mathrm{Dy}$ reaction at 65 MeV, observing the resulting γ-ray transitions with the Gammasphere array. The even- and odd-spin members of the $K^{\pi }=2^{+}$γ band are observed up to ${32}^{+}$ and ${31}^{+}$, respectively. This rotational band faithfully tracks the ground-state configuration to the highest spins. The members of a possible γ vibration built on the aligned yrast $S$ band are observed up to spins ${28}^{+}$ and ${27}^{+}$. An even-spin positive-parity band, observed up to spin ${24}^{+}$, is a candidate for an aligned $S$ band built on the seniority-zero configuration of the $0_2^{+}$ state at 676 keV. The crossing of this band with the $0_2^{+}$ band is at $\hslash {\omega }_c=0.28\left(1\right)\mathrm{MeV}$ and is consistent with the configuration of the $0_2^{+}$ band not producing any blocking of the monopole pairing.

We obtain wave functions for two protons and two neutrons in the $g_{9/2}$ shell expressed as column vectors with amplitudes $D(J_p,J_n)$. When we use a quadrupole-quadrupole interaction $\left(Q·Q\right)$ we get, in many cases, a very strong overlap with wave functions given by a single set of unitary 9-$j$ coefficients—$\mathrm{U}9j=\langle {\left(jj\right)}^{2j}{\left(j{j}^{J_B}\right|{\left(jj\right)}^{J_p}{\left(jj\right)}^{J_n})}^I\rangle$. Here $J_B=9$ for even $IT=0$ states. For both even and odd $T=1$ states we take $J_B$ equal to 8 whilst for odd $I,T=0$ we take $J_B$ to be 7. We compare the $Q·Q$ results with those of a more realistic interaction.

Background: Nuclear excited states within a wide range of excitation energies are formally described by linear response theory. Besides its conventional formulation within the quasiparticle random phase approximation representing excited states as two correlated quasiparticles, there exist extensions for four-quasiparticle configurations. Such extended approaches are quite successful in the description of gross properties of nuclear spectra; however, accounting for many of their fine features requires further extension of the configuration space.

Purpose: This work aims at the development of an approach which is capable of such an extension as well as of reproducing and predicting fine spectral properties, which are of special interest at low energies.

Method: The method is based on covariant density functional theory and the time-blocking approximation, which is extended for couplings between quasiparticles and multiphonon excitations.

Results: A covariant multiphonon response theory is developed and adopted for nuclear structure calculations in medium-mass and heavy nuclei. The equations are formulated in both general and coupled forms in the spherical basis.

Conclusions: The developed covariant multiphonon response theory represents a new generation of approaches to nuclear response, which aims at a unified description of both high-frequency collective states and low-energy spectroscopy in medium-mass and heavy nuclei.

We perform transport model calculations for central collisions of mass 120 on mass 120 at laboratory beam energy in the range 20 MeV/nucleon to 200 MeV/nucleon. A simplified yet accurate method allows calculation of fluctuations in systems much larger than what was considered feasible in a well-known and already existing model. The calculations produce clusters. The distribution of clusters is remarkably similar to that obtained in equilibrium statistical model.

Understanding the mechanisms of induced nuclear fission for a broad range of neutron energies could help resolve fundamental science issues, such as the formation of elements in the universe, but could have also a large impact on societal applications in energy production or nuclear waste management. The goal of this paper is to set up the foundations of a microscopic theory to study the static aspects of induced fission as a function of the excitation energy of the incident neutron, from thermal to fast neutrons. To account for the high excitation energy of the compound nucleus, we employ a statistical approach based on finite temperature nuclear density functional theory with Skyrme energy densities, which we benchmark on the ${}^{239}\mathrm{Pu}$($n,f$) reaction. We compute the evolution of the least-energy fission pathway across multidimensional potential energy surfaces with up to five collective variables as a function of the nuclear temperature and predict the evolution of both the inner and the outer fission barriers as a function of the excitation energy of the compound nucleus. We show that the coupling to the continuum induced by the finite temperature is negligible in the range of neutron energies relevant for many applications of neutron-induced fission. We prove that the concept of quantum localization introduced recently can be extended to $T>0$, and we apply the method to study the interaction energy and total kinetic energy of fission fragments as a function of the temperature for the most probable fission. While large uncertainties in theoretical modeling remain, we conclude that a finite temperature nuclear density functional may provide a useful framework to obtain accurate predictions of fission fragment properties.

The purpose of this article is to derive the analytic expression for the angular-momentum dependence ($I$ dependence) of the moment of inertia in microscopic mean-field theory for both even-even and odd-mass nuclei. Based on the constrained Hartree-Fock-Bogoliubov theory, the Coriolis antipairing effect is taken into account as the second-order perturbation to the BCS basis together with the blocking effect. Instead of integration, an asymptotic series expansion is applied to the quantity in which finiteness of the nuclear system becomes tangible in the high-spin region, where the gap parameter $\Delta$ becomes much smaller than the average single-particle level distance $d$. As a result, $\Delta$ keeps a small but finite value even for high-spin states, showing that there is no sharp phase transition in the nucleus. Analytic formulas are derived for the $I$ dependence of the moment of inertia for different regions of $\Delta \ge d/2$ and $\Delta <d/2$.

The half-life of the isospin $T=1/2$ mirror ${\beta }^{+}$ decay of ${}^{21}\mathrm{Na}$ was measured at the GANIL-SPIRAL radioactive ion beam facility to be $T_{1/2}=22.422$ (10) s, a result that is more than a factor of 5 times more precise than the previous world average, with a resulting $ft$ value that is now two times more precise. The precision of this new result implies that the half-life is no longer the dominant source of uncertainty in the $\mathcal{F}t$ value used in the calculation of $V_{\mathrm{ud}}$ from mirror decays to test the conserved vector current hypothesis of the standard model. The value of $V_{\mathrm{ud}}$ deduced from mirror decays using the new half-life result is now in better agreement with the $V_{\mathrm{ud}}$ derived from $T=1$ superallowed $0^{+}$ to $0^{+}$ transitions.

The formalism based on correlated basis functions and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground-state energy, the effective mass, and the momentum distribution, shows that the effective-interaction approach is quite accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.

The origin of the nuclear tensor interaction in the covariant energy density functional (EDF) is presented in this work, associated with the Fock diagrams of Lorentz scalar and vector couplings. With this newly obtained relativistic formalism of the nuclear tensor interaction, more distinct tensor effects are found in the Fock diagrams of the Lorentz scalar and vector couplings, as compared to the Lorentz pseudovector and tensor channels. A unified and self-consistent treatment of both the nuclear tensor and spin-orbit interactions, which dominate the spin-dependent features of the nuclear force, is then achieved by the relativistic models. Moreover, careful analysis of the tensor strengths indicates the reliability of the nuclear tensor interaction in the covariant EDF for exploring the nuclear structure, excitation, and decay modes.

A simple potential model of the Hulthen type without spin-orbit coupling is considered as the ground-state interaction, and in conjunction with supersymmetric quantum mechanics, higher partial-wave interactions are developed to study the scattering of nucleons from light nuclei. The phase function method is adopted to deal with scattering phase shifts. Applying certain energy-dependent correction factors to our interactions, a close agreement with experimental data is obtained for the elastic scattering of nucleons from alpha particles up to 12 MeV.

Background: The barrier distribution function is an important observable in low-energy nucleus-nucleus collisions because it carries the distinct signature of the channel-coupling effect that is dominant at low energies. It can be derived from the fusion excitation function as well as from the back-angle quasi-elastic excitation function. The barrier distribution functions derived from the two complimentary measurements, in general, appear to peak at an energy close to the Coulomb barrier for strongly bound systems. But for weakly bound projectiles, like ${}^6\mathrm{Li}$, a relative shift is observed between the distributions.

Purpose: The present work investigates the barrier distribution functions from fusion as well as from the back-angle quasi-elastic excitation function for the ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ system. The purpose is to look for the existence of a shift, if any, between the two measured distribution functions, as reported for ${}^6\mathrm{Li}$ collision with heavy targets. A detailed coupled-channel calculation to probe the behavior of the distribution functions and their relative shift has been attempted.

Measurement: A simultaneous measurement of fusion and back-angle quasi-elastic excitation functions for the system ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ was performed. The fusion excitation function was measured for the energy range of 11 to 28 MeV while the quasi-elastic excitation function measurement extended from 11 to 20 MeV. The barrier distribution functions were subsequently extracted from both the excitation functions and compared.

Results: A small shift of around 450 keV peak to peak is observed between the barrier distribution functions derived from the complementary measurements. Detailed coupled channel and coupled reaction channel calculations reproduced both the excitation functions and barrier distributions. The shift of about 550 keV resulted from the model predictions corroborate the experimentally observed value for ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ system.

Conclusions: The coupling to inelastic channels are found to be sufficient to describe the fusion-barrier distribution. The positive $Q$-value one-proton and one-neutron stripping channels, leading to three-body final states, on the other hand, play dominant roles in reproducing the barrier distribution from the back-angle quasi-elastic excitation function.

We report the results of the femtoscopic analysis of pairs of identical pions measured in $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. Femtoscopic radii are determined as a function of event multiplicity and pair momentum in three spatial dimensions. As in the $pp$ collision system, the analysis is complicated by the presence of sizable background correlation structures in addition to the femtoscopic signal. The radii increase with event multiplicity and decrease with pair transverse momentum. When taken at comparable multiplicity, the radii measured in $p$-Pb collisions, at high multiplicity and low pair transverse momentum, are 10%–20% higher than those observed in $pp$ collisions but below those observed in $A-A$ collisions. The results are compared to hydrodynamic predictions at large event multiplicity as well as discussed in the context of calculations based on gluon saturation.

We extend our recent study of shape evolution, collective excitation spectra, and decay properties of transactinide nuclei [V. Prassa, T. Nikšić, and D. Vretenar, Phys. Rev. C 88, 044324 (2013)], based on the microscopic framework of relativistic energy density functionals, to two-quasiparticle (2qp) excitations in the axially deformed Rf, Sg, Hs, and Ds isotopes, with neutron number $N=160–166$. The evolution of high-$K$ isomers is analyzed in a self-consistent axially symmetric relativistic Hartree-Bogoliubov calculation using the blocking approximation with time-reversal symmetry breaking. The occurrence of a series of low-energy high-$K$ isomers is predicted, in particular the $9_{\nu }^{-}$ in the $N=160$ and $N=166$ isotopes, and the ${12}_{\nu }^{-}$ in the $N=164$ nuclei. The effect of the $N=162$ deformed-shell closure on the excitation of 2qp states is discussed. In the $N=162$ isotones we find a relatively low density of 2qp states, with no two-neutron states below 1.6 MeV excitation energy and two-proton states at $\approx 0.5$ MeV higher energy than the lowest 2qp states in neighboring isotopes. This is an interesting result that can be used to characterise the occurrence of deformed shell gaps in very heavy nuclei.

The phase space obtained using the isospin quantum molecular dynamical (IQMD) model is analyzed by applying the binding energy cut in the most commonly and widely used secondary cluster recognition algorithm. In addition, for the present study, the energy contribution from momentum-dependent and symmetry potentials is also included during the calculation of total binding energy, which was absent in clusterization algorithms used earlier. The stability of fragments and isospin effects are explored by using the new clusterization algorithm. The findings are summarized as follows: (1) The clusterization algorithm identifies the fragments at quite early time. (2) It is more sensitive for free nucleons and light charged particles compared to intermediate mass fragments, which results in the enhanced (reduced) production of free nucleons (light charged particles, or LCPs). (3) It has affected the yield of isospin-sensitive observables—neutrons ($n$), protons ($p$), ${}^3\mathrm{H},{}^3\mathrm{He}$, and the single ratio $\left[R\right(n/p\left)\right]$—to a greater extent in the mid-rapidity and low kinetic energy region. In conclusion, the inclusion of the binding energy cut in the clusterization algorithm is found to play a crucial role in the study of isospin physics. This study will give another direction for the determination of symmetry energy in heavy-ion collisions at intermediate energies.

After a successful attempt to define and determine recently the compound nucleus (CN) fusion/ formation probability $P_{\text{CN}}$ within the dynamical cluster-decay model (DCM), we introduce and estimate here for the first time the survival probability $P_{\text{surv}}$ of CN against fission, again within the DCM. Calculated as the dynamical fragmentation process, $P_{\text{surv}}$ is defined as the ratio of the evaporation residue (ER) cross section ${\sigma }_{\text{ER}}$ and the sum of ${\sigma }_{\text{ER}}$ and fusion-fission (ff) cross section ${\sigma }_{\text{ff}}$, the CN formation cross section ${\sigma }_{\text{CN}}$, where each contributing fragmentation cross section is determined in terms of its formation and barrier penetration probabilities $P_0$ and $P$. In DCM, the deformations up to hexadecapole and “compact” orientations for both in-plane (coplanar) and out-of-plane (noncoplanar) configurations are allowed. Some 16 “hot” fusion reactions, forming a CN of mass number $A_{\text{CN}}\sim 100$ to superheavy nuclei, are analyzed for various different nuclear interaction potentials, and the variation of $P_{\text{surv}}$ on CN excitation energy $E^{*}$, fissility parameter $\chi$, CN mass $A_{\text{CN}}$, and Coulomb parameter $Z_1{Z}_2$ is investigated. Interesting results are that three groups, namely, weakly fissioning, radioactive, and strongly fissioning superheavy nuclei, are identified with $P_{\text{surv}}$, respectively, $\sim 1,\sim {10}^{-6}$, and $\sim {10}^{-10}$. For the weakly fissioning group ($100<A_{\text{CN}}\lesssim 200$), independent of the interaction potential, different isotopes and for coplanar or noncoplanar collisions, $P_{\text{surv}}$ decreases from one to zero as $E^{*}$ increases, whereas, independent of entrance channel effects, the same is surprisingly the reverse for the radioactive group ($A_{\text{CN}}\sim 200–250$), i.e., $P_{\text{surv}}$ increases with the increase of $E^{*}$. This is shown to be so due to the different relative magnitudes of ${\sigma }_{\text{ER}}$ and ${\sigma }_{\text{ff}}$ and their variations with $E^{*}$ in the two cases. For the superheavy nuclei also $P_{\text{surv}}$ is a decreasing function of $E^{*}$. Furthermore, of particular interest are the cases of ${}^{105}{\mathrm{Ag}}^{*}$, isotopes of ${\mathrm{Pt}}^{*}$, and ${}^{213,215,217}{\mathrm{Fr}}^{*}$ nuclei — for ${}^{105}{\mathrm{Ag}}^{*}$, whereas the $P_{\text{CN}}$ belongs to the strongly fissioning superheavy group, $P_{\text{surv}}$ belongs to weakly fissioning nuclei; for ${\mathrm{Pt}}^{*}$ isotopes, the inverse of all the compound systems studied, both $P_{\text{CN}}$ and $P_{\text{surv}}$ decrease with the increase of $E^{*}$; for ${}^{213,215,217}{\mathrm{Fr}}^{*}$ nuclei, though fissility $\chi$ is nearly the same, $P_{\text{surv}}$ for ${}^{213,217}{\mathrm{Fr}}^{*}$ is of the same order as for weakly fissioning nuclei, but that for ${}^{215}{\mathrm{Fr}}^{*}$ is of the order of radioactive nuclei. Apparently, further calculations are called for.

Background: Theoretical calculations have shown that the energy and angular correlations in the three-body decay of the two-neutron unbound ${}^{26}\mathrm{O}$ can provide information on the ground-state wave function, which has been predicted to have a dineutron configuration and $2n$ halo structure.

Purpose: To use the experimentally measured three-body correlations to gain insight into the properties of ${}^{26}\mathrm{O}$, including the decay mechanism and ground-state resonance energy.

Method: ${}^{26}\mathrm{O}$ was produced in a one-proton knockout reaction from ${}^{27}\mathrm{F}$ and the ${}^{24}\mathrm{O}+n+n$ decay products were measured using the MoNA-Sweeper setup. The three-body correlations from the ${}^{26}\mathrm{O}$ ground-state resonance decay were extracted. The experimental results were compared to Monte Carlo simulations in which the resonance energy and decay mechanism were varied.

Results: The measured three-body correlations were well reproduced by the Monte Carlo simulations but were not sensitive to the decay mechanism due to the experimental resolutions. However, the three-body correlations were found to be sensitive to the resonance energy of ${}^{26}\mathrm{O}$. A $1\sigma$ upper limit of 53 keV was extracted for the ground-state resonance energy of ${}^{26}\mathrm{O}$.

Conclusions: Future attempts to measure the three-body correlations from the ground-state decay of ${}^{26}\mathrm{O}$ will be very challenging due to the need for a precise measurement of the ${}^{24}\mathrm{O}$ momentum at the reaction point in the target.

Event-by-event fluctuations of the multiplicities of inclusive charged particles and photons at forward rapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV have been studied. The dominant contribution to such fluctuations is expected to come from correlated production of charged and neutral pions. We search for evidence of dynamical fluctuations of different physical origins. Observables constructed out of moments of multiplicities are used as measures of fluctuations. Mixed events and model calculations are used as base lines. Results are compared to the dynamical net-charge fluctuations measured in the same acceptance. A nonzero statistically significant signal of dynamical fluctuations is observed in excess to the model prediction when charged particles and photons are measured in the same acceptance. We find that, unlike dynamical net-charge fluctuation, charge-neutral fluctuation is not dominated by correlation owing to particle decay. Results are compared to the expectations based on the generic production mechanism of pions owing to isospin symmetry, for which no significant ($<1\%$) deviation is observed.

We investigate the $\gamma p\to \varphi K^{+}\Lambda$ reaction near threshold within an effective Lagrangian approach and the isobar model. Various nucleon resonances caused by the $\pi$ and $\eta$ meson exchanges and background contributions are considered. It is shown that the contribution from the $N^{*}\left(1535\right)$ resonance caused by the $\eta$ meson exchange plays the predominant role. Hence, this reaction provides a good new platform to study the $N^{*}\left(1535\right)$ resonance. The predicted total cross section and specific features of the angular distributions can be tested by future experiments.

Time-of-flight spectra of the neutron capture events of ${}^{142}\mathrm{Nd}$ were measured using a spallation neutron source at the Japan Proton Accelerator Research Complex. The first six resonances of ${}^{142}\mathrm{Nd}$ reported in a previous work were not observed. The experimental results and cross-search of resonance energies in nuclear data libraries suggested that resonances of the impurity nuclide ${}^{141}\mathrm{Pr}$ have been mistakenly assigned as ${}^{142}\mathrm{Nd}$ in the previous experiment. To investigate the impact of the nonexistence of the resonances on the $s$-process nucleosynthesis model, the Maxwellian averaged neutron capture cross sections with and without the misassigned resonances were compared.